Meem loves ice cream cones. So much so that she created an ice cream stand to share the joy of ice creams among all people. However, the ice cream man she assigned to make the cones doesn't share the same view as her. His only goal is to maximize profit. While preparing the ice cream, he doesn't even fill up the cone. Instead, he puts one scoop (a specialized spherical spoon used to serve ice cream on a cone) of vanilla on the cone (as seen in the side view of the cone below). He even makes the volume of the cone as small as possible. This made the ice cream lovers who bought ice cream from Meem's ice cream stand very sad.
Meem found this out. To compensate for the less amount of ice cream put on the cone, she wants to fill up the rest of the cone with liquid chocolate. But she doesn't know anything about the size of the cone. She found the scoop that is used to pour vanilla in the cone. She measured the radius of the scoop, $R$. Now your task is to help her calculate the amount of liquid chocolate required to fill up the cone.
For simplicity, assume that they use a right circular cone and the cone is circumscribed about the sphere (as shown in the image). A right circular cone is a cone whose base is a circle and there is a line perpendicular to the base through its center which passes through the apex of the cone. Use $π = 3.141592653589$ if needed. The thickness of the scoop is negligible.
Input starts with an integer $T$ ($1 \le T \le 25$), denoting the number of test cases. The next $T$ lines contain a single real number $R$ ($0 < R \le 100$) denoting the radius of the scoop.
For each case of input, you have to print the required amount in a newline. Errors less than $10^{-6}$ will be ignored.
Input | Output |
---|---|
1 3 | 113.09733553 |